FIG. 1 illustrates cellular network 100 of the prior art. Each cell 102a-c in cellular network 100 is generally defined by an area in which base stations 104a-c are able to communicate with User Equipment (UE) 106a-d. Examples of UEs 106a-d include telephones, smartphones, Personal Data Assistants (PDAs), tablet computers, cellular data devices for use with laptop computers, and the like. Generally, each cell 102a-c includes one corresponding base station 104a-c. 
Any number of UEs 106a-d may be found in cells 102a-c, depending on the use habits of the users of cellular network 100. For example, cell 102b includes two UEs 106c-d. In such an embodiment, both UEs 106c-d may communicate with base station 104b at the same time. Depending on the protocol used by base station 104b, UEs 106c-d may communicate simultaneously, or substantially simultaneously. Alternatively, UEs 106c-d may communicate with base station 104b within a time slot. Additionally, UEs 106a-d may move between cells as the user travels from one area to another. As shown, UE 106a may move from cell 102a to cell 102c. In this sort of case, cell 102a includes two UEs 106a-b initially, but once UE 102a moves to cell 102c, cell 102a only includes UE 106b. Thus cellular networks 100 are generally dynamic in nature, and changes in the topology of cellular network 100 may be random, based upon the user's habits.
FIG. 2 illustrates an example of a topology for any of cells 102a-c. In addition to base station 104, cells 102 may include antenna 202 coupled to base station 104. Antenna 202 receives random access signals from UEs 106 operated by user 204 in a multipath environment and mobile user 206 over Random Access Channels (RACHs) operated by base station 104. The RACH allows UEs 106 to gain initial access to cellular network 100 and facilitates uplink synchronization.
FIG. 3 illustrates RACH detection circuit 300 according to the prior art. RACH detection circuit 300 is often included in base station 104. RACH detection circuit 300 includes CP removal module 302 for removing the Cyclic Prefix (CP) from received symbols. RACH detection circuit 300 also includes downsampling/resampling module 304 for reducing a sample rate to a frequency that is suitable for use by correlator 306. The reduced sample rate simplifies operations of the correlator 306, particularly in FFT module 308. Correlator 306 includes Fast Fourier Transform (FFT) module 308 configured to transform the downsampled symbol into frequency domain, correlator 306 also includes subcarrier demapping module 310 and multiplier 312. Multiplier 312 multiplies the demapped subcarriers with a conjugate of a root sequence in the frequency domain. The multiplication result is then converted back to time domain by Inverse Discrete Fourier Transform (IDFT) module 314. In prior systems 300, signature detection and timing offset estimation module 316 detects a random access signal from UE 106 and determines the timing offset of the detected random access signal.
Unfortunately, as described below, RACH detection circuit 300 generates a large number of false alarms. A false alarm is an event that is a result of a RACH detection circuit detecting energy that is outside of the boundary of a signature sent by UE 106c. For example, when a UE 106c is very close to a base station 104b, the timing offset may be very low. In such an embodiment, power leakage from a random access signal sent by UE 106c to base station 104 may fall outside of detection interval for a first signature and fall within a signal detection interval of a second signature. Thus, the power leakage may appear to be a second random access signal from a second UE 106d. Such situations may trigger false alarm events.
Additionally, noise, interference, frequency offset and Doppler shifts may all contribute to false detections. For example, in a second situation, UE 106a may be far from base station 104c. Thus, the time delay may be large. If UE 106a is in a multipath environment, for example, then the multipath reflections may cross into a detection interval for a second signature. Because of the time shift, RACH detection circuit 300 may experience a false alarm because random access signals may appear to be from two separate UEs 106 to RACH detection circuit 300.
In cellular systems, UEs 106a-d send random access signals to base stations 104a-c to gain initial network access to cell network 100. Ideally base station 104a-c would detect the random access signals with high detection accuracy while maintaining a low false alarm rate. Currently, two primary methods are used by base stations for detection of random access signals. The first is a full frequency-domain method for achieving a high level of accuracy. Unfortunately, most common RACH detection circuits 300 are not able to perform full frequency-domain analysis because of the complexity of the FFT and high system resources requirements associated with such methods. The second method for detection includes down-sampling to significantly reduce hardware complexity while achieving a minimum level of acceptable performance. Unfortunately, the minimum level of acceptable performance is still not particularly accurate, and there is much room for improvement. Both of these approaches detect fake random access signals, thus causing a high false alarm rate under some circumstances.